Asymptotic normality for U-statistics of associated random variables

Abstract

Let {X_n, n^≥1} be a stationary sequence of associated random variables and U_n be a U-statistic based on this sample. We establish a central limit theorem for U_n when the U-statistic is degenerate or non-degenerate using an orthogonal expansion for the kernel associated with U_n. We extend the results to U-statistics of kernels of degree 3 and to V-statistics of arbitrary degree. We also establish a central limit theorem for the two sample U-statistic based on observations of two independent stationary associated sequences.